Bayesian Statistics: An Introduction, 4th Edition

4.5 Point null hypotheses for the normal distribution

4.5.1 Calculation of the Bayes’ factor

Suppose is a vector of independently random variables, and that is known. Because of the remarks at the end of the last section, we can work entirely in terms of the sufficient statistic

We have to make some assumption about the density of θ under the alternative hypothesis, and clearly one of the most natural things to do is to suppose that this density is normal, say . Strictly, this should be regarded as a density on values of θ other than , but when probabilities are found by integration of this density, the odd point will make no difference. It will usually seem sensible to take as, presumably, ...